Planning system for speed limit changes for autonomous vehicles

ABSTRACT

In one embodiment, a speed planning system receives speed limit information for an autonomous driving vehicle (ADV), where the speed limit information includes a change in road speed limit for a current road of the ADV. The system determines a tapered speed limit corresponding to the current road based on the speed limit information, where the tapered speed limit correspond to a gradual speed reduction from a first road speed limit to a second road speed limit. The system determines a cost function based on the tapered speed limit and the first and second road speed limits. The system generates a number of trajectory candidates based on the cost function. The system selects a trajectory based on the trajectory candidates to control the ADV using the selected trajectory.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to operatingautonomous driving vehicles. More particularly, embodiments of thedisclosure relate to a planning system for speed limit changes forautonomous driving vehicles (ADV).

BACKGROUND

Vehicles operating in an autonomous mode (e.g., driverless) can relieveoccupants, especially the driver, from some driving-relatedresponsibilities. When operating in an autonomous mode, the vehicle cannavigate to various locations using onboard sensors, allowing thevehicle to travel with minimal human interaction or in some caseswithout any passengers.

Motion planning and control are critical operations in autonomousdriving. However, conventional motion planning operations estimate thedifficulty of completing a given path mainly from its curvature andspeed, without considering the differences in features for differenttypes of vehicles. Same motion planning and control is applied to alltypes of vehicles, which may not be accurate and smooth under somecircumstances.

Speed limits are generally indicated on a traffic sign expressed askilometers per hour (km/h) reflecting the legal maximum or minimum speedroad vehicles may travel on a given segment of road. Some county/cityroads have a legally assigned maximum speed limit even when no speedlimit indications are present.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure are illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 is a block diagram illustrating a networked system according toone embodiment.

FIG. 2 is a block diagram illustrating an example of an autonomousdriving vehicle according to one embodiment.

FIGS. 3A-3B are block diagrams illustrating an example of an autonomousdriving system used with an autonomous driving vehicle according to oneembodiment.

FIG. 4 is a block diagram illustrating an example of a decision andplanning system according to one embodiment.

FIG. 5 is a block diagram illustrating a station-lateral map accordingto one embodiment.

FIGS. 6A and 6B are block diagrams illustrating station-time mapsaccording to some embodiments.

FIGS. 7A-7B are block diagrams illustrating speed versus distance plotsfor a change in speed limit according to some embodiments.

FIGS. 8A-8B are block diagrams illustrating station-time maps accordingto some embodiments.

FIG. 9 is a block diagram illustrating a speed limit module according toone embodiment.

FIG. 10 is a flow diagram illustrating a speed planning with gradualspeed limits method according to one embodiment.

FIG. 11 is a block diagram illustrating a tapered speed limits generatoraccording to one embodiment.

FIG. 12 is a flow diagram illustrating a method to generate gradualspeed limits according to one embodiment.

DETAILED DESCRIPTION

Various embodiments and aspects of the disclosures will be describedwith reference to details discussed below, and the accompanying drawingswill illustrate the various embodiments. The following description anddrawings are illustrative of the disclosure and are not to be construedas limiting the disclosure. Numerous specific details are described toprovide a thorough understanding of various embodiments of the presentdisclosure. However, in certain instances, well-known or conventionaldetails are not described in order to provide a concise discussion ofembodiments of the present disclosures.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin conjunction with the embodiment can be included in at least oneembodiment of the disclosure. The appearances of the phrase “in oneembodiment” in various places in the specification do not necessarilyall refer to the same embodiment.

Posted legal maximum (or minimum) road speed limits guide an operator toslow down (or speed up) a vehicle for safety purposes. For an autonomousvehicle (ADV), the posted speed limits can be determined by perceivingan environment of the ADV. The posted speed limits can further beretrieved from a map data based on a current road of the ADV. Here, themap data is preconfigured with the posted speed limit information.

When the posted speed limit for a road suddenly drops, e.g., from 100 to40 km/h, as in the case of a freeway exit-ramp or a sharp turn, an ADVtypically applies a sharp brake control to stay within the next postedspeed limit. The following embodiments dampens the sudden sharp brakecontrol.

According to a first aspect, a speed planning system receives speedlimit information for an autonomous driving vehicle (ADV), where thespeed limit information includes a change in road speed limit for acurrent road of the ADV. The system determines a tapered speed limitcorresponding to the current road based on the speed limit information,where the tapered speed limit correspond to a gradual speed reductionfrom a first road speed limit to a second road speed limit. The systemdetermines a cost function based on the tapered speed limit and thefirst and second road speed limits. The system generates a number oftrajectory candidates based on the cost function. The system selects atrajectory based on the trajectory candidates to control the ADV usingthe selected trajectory.

According to a second aspect, a system determines a reference speedcurve to gradually slow down an autonomous driving vehicle (ADV). Foreach section (or segment) of a plurality of road sections in mapinformation for an ADV, the system determines a reduction in speed limitfor the road section from a first speed limit to a second speed limit.The system generates a tapered speed limit for the road section from thefirst speed limit to the second speed limit based on the reference speedcurve. The system stores the tapered speed limit for the section of roadin the map information, where the tapered speed limit is used by the ADVto generate driving trajectory candidates.

FIG. 1 is a block diagram illustrating an autonomous driving networkconfiguration according to one embodiment of the disclosure. Referringto FIG. 1 , network configuration 100 includes autonomous drivingvehicle (ADV) 101 that may be communicatively coupled to one or moreservers 103-104 over a network 102. Although there is one ADV shown,multiple ADVs can be coupled to each other and/or coupled to servers103-104 over network 102. Network 102 may be any type of networks suchas a local area network (LAN), a wide area network (WAN) such as theInternet, a cellular network, a satellite network, or a combinationthereof, wired or wireless. Server(s) 103-104 may be any kind of serversor a cluster of servers, such as Web or cloud servers, applicationservers, backend servers, or a combination thereof. Servers 103-104 maybe data analytics servers, content servers, traffic information servers,map and point of interest (MPOI) servers, or location servers, etc.

An ADV refers to a vehicle that can be configured to in an autonomousmode in which the vehicle navigates through an environment with littleor no input from a driver. Such an ADV can include a sensor systemhaving one or more sensors that are configured to detect informationabout the environment in which the vehicle operates. The vehicle and itsassociated controller(s) use the detected information to navigatethrough the environment. ADV 101 can operate in a manual mode, a fullautonomous mode, or a partial autonomous mode.

In one embodiment, ADV 101 includes, but is not limited to, autonomousdriving system (ADS) 110, vehicle control system 111, wirelesscommunication system 112, user interface system 113, and sensor system115. ADV 101 may further include certain common components included inordinary vehicles, such as, an engine, wheels, steering wheel,transmission, etc., which may be controlled by vehicle control system111 and/or ADS 110 using a variety of communication signals and/orcommands, such as, for example, acceleration signals or commands,deceleration signals or commands, steering signals or commands, brakingsignals or commands, etc.

Components 110-115 may be communicatively coupled to each other via aninterconnect, a bus, a network, or a combination thereof. For example,components 110-115 may be communicatively coupled to each other via acontroller area network (CAN) bus. A CAN bus is a vehicle bus standarddesigned to allow microcontrollers and devices to communicate with eachother in applications without a host computer. It is a message-basedprotocol, designed originally for multiplex electrical wiring withinautomobiles, but is also used in many other contexts.

Referring now to FIG. 2 , in one embodiment, sensor system 115 includes,but it is not limited to, one or more cameras 211, global positioningsystem (GPS) unit 212, inertial measurement unit (IMU) 213, radar unit214, and a light detection and range (LIDAR) unit 215. GPS system 212may include a transceiver operable to provide information regarding theposition of the ADV. IMU unit 213 may sense position and orientationchanges of the ADV based on inertial acceleration. Radar unit 214 mayrepresent a system that utilizes radio signals to sense objects withinthe local environment of the ADV. In some embodiments, in addition tosensing objects, radar unit 214 may additionally sense the speed and/orheading of the objects. LIDAR unit 215 may sense objects in theenvironment in which the ADV is located using lasers. LIDAR unit 215could include one or more laser sources, a laser scanner, and one ormore detectors, among other system components. Cameras 211 may includeone or more devices to capture images of the environment surrounding theADV. Cameras 211 may be still cameras and/or video cameras. A camera maybe mechanically movable, for example, by mounting the camera on arotating and/or tilting a platform.

Sensor system 115 may further include other sensors, such as, a sonarsensor, an infrared sensor, a steering sensor, a throttle sensor, abraking sensor, and an audio sensor (e.g., microphone). An audio sensormay be configured to capture sound from the environment surrounding theADV. A steering sensor may be configured to sense the steering angle ofa steering wheel, wheels of the vehicle, or a combination thereof. Athrottle sensor and a braking sensor sense the throttle position andbraking position of the vehicle, respectively. In some situations, athrottle sensor and a braking sensor may be integrated as an integratedthrottle/braking sensor.

In one embodiment, vehicle control system 111 includes, but is notlimited to, steering unit 201, throttle unit 202 (also referred to as anacceleration unit), and braking unit 203. Steering unit 201 is to adjustthe direction or heading of the vehicle. Throttle unit 202 is to controlthe speed of the motor or engine that in turn controls the speed andacceleration of the vehicle. Braking unit 203 is to decelerate thevehicle by providing friction to slow the wheels or tires of thevehicle. Note that the components as shown in FIG. 2 may be implementedin hardware, software, or a combination thereof.

Referring back to FIG. 1 , wireless communication system 112 is to allowcommunication between ADV 101 and external systems, such as devices,sensors, other vehicles, etc. For example, wireless communication system112 can wirelessly communicate with one or more devices directly or viaa communication network, such as servers 103-104 over network 102.Wireless communication system 112 can use any cellular communicationnetwork or a wireless local area network (WLAN), e.g., using WiFi tocommunicate with another component or system. Wireless communicationsystem 112 could communicate directly with a device (e.g., a mobiledevice of a passenger, a display device, a speaker within vehicle 101),for example, using an infrared link, Bluetooth, etc. User interfacesystem 113 may be part of peripheral devices implemented within vehicle101 including, for example, a keyboard, a touch screen display device, amicrophone, and a speaker, etc.

Some or all of the functions of ADV 101 may be controlled or managed byADS 110, especially when operating in an autonomous driving mode. ADS110 includes the necessary hardware (e.g., processor(s), memory,storage) and software (e.g., operating system, planning and routingprograms) to receive information from sensor system 115, control system111, wireless communication system 112, and/or user interface system113, process the received information, plan a route or path from astarting point to a destination point, and then drive vehicle 101 basedon the planning and control information. Alternatively, ADS 110 may beintegrated with vehicle control system 111.

For example, a user as a passenger may specify a starting location and adestination of a trip, for example, via a user interface. ADS 110obtains the trip related data. For example, ADS 110 may obtain locationand route data from an MPOI server, which may be a part of servers103-104. The location server provides location services and the MPOIserver provides map services and the POIs of certain locations.Alternatively, such location and MPOI information may be cached locallyin a persistent storage device of ADS 110.

While ADV 101 is moving along the route, ADS 110 may also obtainreal-time traffic information from a traffic information system orserver (TIS). Note that servers 103-104 may be operated by a third partyentity. Alternatively, the functionalities of servers 103-104 may beintegrated with ADS 110. Based on the real-time traffic information,MPOI information, and location information, as well as real-time localenvironment data detected or sensed by sensor system 115 (e.g.,obstacles, objects, nearby vehicles), ADS 110 can plan an optimal routeand drive vehicle 101, for example, via control system 111, according tothe planned route to reach the specified destination safely andefficiently.

Server 103 may be a data analytics system to perform data analyticsservices for a variety of clients. In one embodiment, data analyticssystem 103 includes data collector 121 and machine learning engine 122.Data collector 121 collects driving statistics 123 from a variety ofvehicles, either ADVs or regular vehicles driven by human drivers.Driving statistics 123 include information indicating the drivingcommands (e.g., throttle, brake, steering commands) issued and responsesof the vehicles (e.g., speeds, accelerations, decelerations, directions)captured by sensors of the vehicles at different points in time. Drivingstatistics 123 may further include information describing the drivingenvironments at different points in time, such as, for example, routes(including starting and destination locations), MPOIs, road conditions,weather conditions, etc.

Based on driving statistics 123, machine learning engine 122 generatesor trains a set of rules, algorithms, and/or predictive models 124 for avariety of purposes. In one embodiment, algorithms 124 may include costfunctions to generate planning trajectories based on a tapered speedlimit in conjunction with posted road speed limits. The tapered speedlimit can be a soft constraint (posted road speed limits are hardconstraints) and is generated based on the posted road speed limits toguide an ADV for a smoother drive. Algorithms 124 can then be uploadedon ADVs to be utilized during autonomous driving in real-time.

Tapered speed limit generator 125 can generate a number of tapered speedlimits for each road segments. Similar to the posted road speed limits,the tapered speed limits indicate a maximum (or minimum) speed limit forthe segment of the road, but only as a soft constraint (a constraintthat is not absolutely enforced) for an ADV. The tapered speed limitscan be stored in speed limit information (e.g., as part of map & routedata 311 and/or speed limits information 313 of FIG. 3A) or as a softconstraint to be used by an ADV to generate one or more drivingtrajectories for the ADV. For example, the tapered speed limits caninclude one or more speed limits gradually reduces from a higher (e.g.,100 km/h) to a lower speed (e.g., 40 km/h) limit along segments of aroad. The tapered speed limits can be used by the ADV to generate/selecta driving trajectory to slow down the ADV from the higher to the lowerspeed limits, with a minimal brake control.

FIGS. 3A and 3B are block diagrams illustrating an example of anautonomous driving system used with an ADV according to one embodiment.System 300 may be implemented as a part of ADV 101 of FIG. 1 including,but is not limited to, ADS 110, control system 111, and sensor system115. Referring to FIGS. 3A-3B, ADS 110 includes, but is not limited to,localization module 301, perception module 302, prediction module 303,decision module 304, planning module 305, control module 306, routingmodule 307, and speed limit module 308.

Some or all of modules 301-308 may be implemented in software, hardware,or a combination thereof. For example, these modules may be installed inpersistent storage device 352, loaded into memory 351, and executed byone or more processors (not shown). Note that some or all of thesemodules may be communicatively coupled to or integrated with some or allmodules of vehicle control system 111 of FIG. 2 . Some of modules301-308 may be integrated together as an integrated module. For example,module 308 may be integrated as a part of planning module 305.

Localization module 301 determines a current location of ADV 300 (e.g.,leveraging GPS unit 212) and manages any data related to a trip or routeof a user. Localization module 301 (also referred to as a map and routemodule) manages any data related to a trip or route of a user. A usermay log in and specify a starting location and a destination of a trip,for example, via a user interface. Localization module 301 communicateswith other components of ADV 300, such as map and route data 311, toobtain the trip related data. For example, localization module 301 mayobtain location and route data from a location server and a map and POI(MPOI) server. A location server provides location services and an MPOIserver provides map services and the POIs of certain locations, whichmay be cached as part of map and route data 311. While ADV 300 is movingalong the route, localization module 301 may also obtain real-timetraffic information from a traffic information system or server.

Based on the sensor data provided by sensor system 115 and localizationinformation obtained by localization module 301, a perception of thesurrounding environment is determined by perception module 302. Theperception information may represent what an ordinary driver wouldperceive surrounding a vehicle in which the driver is driving. Theperception can include the lane configuration, traffic light signals, arelative position of another vehicle, a pedestrian, a building,crosswalk, or other traffic related signs (e.g., stop signs, yieldsigns), etc., for example, in a form of an object. The laneconfiguration includes information describing a lane or lanes, such as,for example, a shape of the lane (e.g., straight or curvature), a widthof the lane, how many lanes in a road, one-way or two-way lane, mergingor splitting lanes, exiting lane, etc.

Perception module 302 may include a computer vision system orfunctionalities of a computer vision system to process and analyzeimages captured by one or more cameras in order to identify objectsand/or features in the environment of the ADV. The objects can includetraffic signals, road way boundaries, other vehicles, pedestrians,and/or obstacles, etc. The computer vision system may use an objectrecognition algorithm, video tracking, and other computer visiontechniques. In some embodiments, the computer vision system can map anenvironment, track objects, and estimate the speed of objects, etc.Perception module 302 can also detect objects based on other sensorsdata provided by other sensors such as a radar and/or LIDAR.

For each of the objects, prediction module 303 predicts what the objectwill behave under the circumstances. The prediction is performed basedon the perception data perceiving the driving environment at the pointin time in view of a set of map/rout information 311 and traffic rules312. For example, if the object is a vehicle at an opposing directionand the current driving environment includes an intersection, predictionmodule 303 will predict whether the vehicle will likely move straightforward or make a turn. If the perception data indicates that theintersection has no traffic light, prediction module 303 may predictthat the vehicle may have to fully stop prior to enter the intersection.If the perception data indicates that the vehicle is currently at aleft-turn only lane or a right-turn only lane, prediction module 303 maypredict that the vehicle will more likely make a left turn or right turnrespectively.

For each of the objects, decision module 304 makes a decision regardinghow to handle the object. For example, for a particular object (e.g.,another vehicle in a crossing route) as well as its metadata describingthe object (e.g., a speed, direction, turning angle), decision module304 decides how to encounter the object (e.g., overtake, yield, stop,pass). Decision module 304 may make such decisions according to a set ofrules such as traffic rules or driving rules 312, which may be stored inpersistent storage device 352.

Routing module 307 is configured to provide one or more routes or pathsfrom a starting point to a destination point. For a given trip from astart location to a destination location, for example, received from auser, routing module 307 obtains route and map information 311 anddetermines all possible routes or paths from the starting location toreach the destination location. Routing module 307 may generate areference line in a form of a topographic map for each of the routes itdetermines from the starting location to reach the destination location.A reference line refers to an ideal route or path without anyinterference from others such as other vehicles, obstacles, or trafficcondition. That is, if there is no other vehicle, pedestrians, orobstacles on the road, an ADV should exactly or closely follows thereference line. The topographic maps are then provided to decisionmodule 304 and/or planning module 305. Decision module 304 and/orplanning module 305 examine all of the possible routes to select andmodify one of the most optimal routes in view of other data provided byother modules such as traffic conditions from localization module 301,driving environment perceived by perception module 302, and trafficcondition predicted by prediction module 303. The actual path or routefor controlling the ADV may be close to or different from the referenceline provided by routing module 307 dependent upon the specific drivingenvironment at the point in time.

Based on a decision for each of the objects perceived, planning module305 plans a path or route for the ADV, as well as driving parameters(e.g., distance, speed, and/or turning angle), using a reference lineprovided by routing module 307 as a basis. That is, for a given object,decision module 304 decides what to do with the object, while planningmodule 305 determines how to do it. For example, for a given object,decision module 304 may decide to pass the object, while planning module305 may determine whether to pass on the left side or right side of theobject. Planning and control data is generated by planning module 305including information describing how vehicle 300 would move in a nextmoving cycle (e.g., next route/path segment). For example, the planningand control data may instruct vehicle 300 to move 10 meters at a speedof 30 miles per hour (mph), then change to a right lane at the speed of25 mph.

Based on the planning and control data, control module 306 controls anddrives the ADV, by sending proper commands or signals to vehicle controlsystem 111, according to a route or path defined by the planning andcontrol data. The planning and control data include sufficientinformation to drive the vehicle from a first point to a second point ofa route or path using appropriate vehicle settings or driving parameters(e.g., throttle, braking, steering commands) at different points in timealong the path or route.

In one embodiment, the planning phase is performed in a number ofplanning cycles, also referred to as driving cycles, such as, forexample, in every time interval of 100 milliseconds (ms). For each ofthe planning cycles or driving cycles, one or more control commands willbe issued based on the planning and control data. That is, for every 100ms, planning module 305 plans a next route segment or path segment, forexample, including a target position and the time required for the ADVto reach the target position. Alternatively, planning module 305 mayfurther specify the specific speed, direction, and/or steering angle,etc. In one embodiment, planning module 305 plans a route segment orpath segment for the next predetermined period of time such as 5seconds. For each planning cycle, planning module 305 plans a targetposition for the current cycle (e.g., next 5 seconds) based on a targetposition planned in a previous cycle. Control module 306 then generatesone or more control commands (e.g., throttle, brake, steering controlcommands) based on the planning and control data of the current cycle.

Note that decision module 304 and planning module 305 may be integratedas an integrated module. Decision module 304/planning module 305 mayinclude a navigation system or functionalities of a navigation system todetermine a driving path for the ADV. For example, the navigation systemmay determine a series of speeds and directional headings to affectmovement of the ADV along a path that substantially avoids perceivedobstacles while generally advancing the ADV along a roadway-based pathleading to an ultimate destination. The destination may be set accordingto user inputs via user interface system 113. The navigation system mayupdate the driving path dynamically while the ADV is in operation. Thenavigation system can incorporate data from a GPS system and one or moremaps so as to determine the driving path for the ADV.

Speed limit module 308 can generate a plurality of speed curves (ortrajectories) based on a speed planning cost function. The speedplanning cost function has components corresponding the posted roadspeed limits (max or min) in conjunction with gradual slow down(tapered) speed limits corresponding to the posted road speed limits.

FIG. 4 is a block diagram illustrating an example of a decision andplanning system according to one embodiment. System 400 may beimplemented as part of autonomous driving system 300 of FIGS. 3A-3B toperform path planning and speed planning operations. Referring to FIG. 4, Decision and planning system 400 (also referred to as a planning andcontrol or PnC system or module) includes, amongst others, routingmodule 307, localization/perception data 401, path decision module 403,speed decision module 405, path planning module 407, speed planningmodule 409, aggregator 411, and trajectory calculator 413.

Path decision module 403 and speed decision module 405 may beimplemented as part of decision module 304. In one embodiment, pathdecision module 403 may include a path state machine, one or more pathtraffic rules, and a station-lateral maps generator. Path decisionmodule 403 can generate a rough path profile as an initial constraintfor the path/speed planning modules 407 and 409 using dynamicprogramming.

In one embodiment, the path state machine includes at least threestates: a cruising state, a changing lane state, and/or an idle state.The path state machine provides previous planning results and importantinformation such as whether the ADV is cruising or changing lanes. Thepath traffic rules, which may be part of driving/traffic rules 312 ofFIG. 3A, include traffic rules that can affect the outcome of a pathdecisions module. For example, the path traffic rules can includetraffic information such as construction traffic signs nearby the ADVcan avoid lanes with such construction signs. From the states, trafficrules, reference line provided by routing module 307, and obstaclesperceived by perception module 302 of the ADV, path decision module 403can decide how the perceived obstacles are handled (i.e., ignore,overtake, yield, stop, pass), as part of a rough path profile.

For example, in one embedment, the rough path profile is generated by acost function consisting of costs based on: a curvature of path and adistance from the reference line and/or reference points to obstacles.Points on the reference line are selected and are moved to the left orright of the reference lines as candidate movements representing pathcandidates. Each of the candidate movements has an associated cost. Theassociated costs for candidate movements of one or more points on thereference line can be solved using dynamic programming for an optimalcost sequentially, one point at a time.

In one embodiment, a state-lateral (SL) maps generator (not shown)generates an SL map as part of the rough path profile. An SL map is atwo-dimensional geometric map (similar to an x-y coordinate plane) thatincludes obstacles information perceived by the ADV. From the SL map,path decision module 403 can lay out an ADV path that follows theobstacle decisions. Dynamic programming (also referred to as a dynamicoptimization) is a mathematical optimization method that breaks down aproblem to be solved into a sequence of value functions, solving each ofthese value functions just once and storing their solutions. The nexttime the same value function occurs, the previous computed solution issimply looked up saving computation time instead of recomputing itssolution.

Speed decision module 405 or the speed decision module includes a speedstate machine, speed traffic rules, and a station-time graphs generator(not shown). Speed decision process 405 or the speed decision module cangenerate a rough speed profile as an initial constraint for thepath/speed planning modules 407 and 409 using dynamic programming. Inone embodiment, the speed state machine includes at least two states: aspeed-up state and/or a slow-down state. The speed traffic rules, whichmay be part of driving/traffic rules 312 of FIG. 3A, include trafficrules that can affect the outcome of a speed decisions module. Forexample, the speed traffic rules can include traffic information such asred/green traffic lights, another vehicle in a crossing route, etc. Froma state of the speed state machine, speed traffic rules, rough pathprofile/SL map generated by decision module 403, and perceivedobstacles, speed decision module 405 can generate a rough speed profileto control when to speed up and/or slow down the ADV. The SL graphsgenerator can generate a station-time (ST) graph as part of the roughspeed profile.

In one embodiment, path planning module 407 includes one or more SLmaps, a geometry smoother, and a path costs module (not shown). The SLmaps can include the station-lateral maps generated by the SL mapsgenerator of path decision module 403. Path planning module 407 can usea rough path profile (e.g., a station-lateral map) as the initialconstraint to recalculate an optimal reference line using quadraticprogramming. Quadratic programming (QP) involves minimizing ormaximizing an objective function (e.g., a quadratic function withseveral variables) subject to bounds, linear equality, and inequalityconstraints.

One difference between dynamic programming and quadratic programming isthat quadratic programming optimizes all candidate movements for allpoints on the reference line at once. The geometry smoother can apply asmoothing algorithm (such as B-spline or regression) to the outputstation-lateral map. The path costs module can recalculate a referenceline with a path cost function, to optimize a total cost for candidatemovements for reference points, for example, using QP optimizationperformed by a QP module (not shown). For example, in one embodiment, atotal path cost function can be defined as follows:pathcost=Σ_(points)(heading)²+Σ_(points)(curvature)²+Σ_(points)(distance)²,where the path costs are summed over all points on the reference line,heading denotes a difference in radial angles (e.g., directions) betweenthe point with respect to the reference line, curvature denotes adifference between curvature of a curve formed by these points withrespect to the reference line for that point, and distance denotes alateral (perpendicular to the direction of the reference line) distancefrom the point to the reference line. In some embodiments, distancerepresents the distance from the point to a destination location or anintermediate point of the reference line. In another embodiment, thecurvature cost is a change between curvature values of the curve formedat adjacent points. Note the points on the reference line can beselected as points with equal distances from adjacent points. Based onthe path cost, the path costs module can recalculate a reference line byminimizing the path cost using quadratic programming optimization, forexample, by the QP module.

Speed planning module 409 includes station-time graphs, a sequencesmoother, and a speed costs module. The station-time graphs can includea ST graph generated by the ST graphs generator of speed decision module405. Speed planning module 409 can use a rough speed profile (e.g., astation-time graph) and results from path planning module 407 as initialconstraints to calculate an optimal station-time curve. The sequencesmoother can apply a smoothing algorithm (such as B-spline orregression) to the time sequence of points. The speed costs module canrecalculate the ST graph with a speed cost function to optimize a totalcost for movement candidates (e.g., speed up/slow down) at differentpoints in time.

For example, in one embodiment, a total speed cost function can be:speed cost=Σ_(points)(speed′)²+Σ_(points)(speed″)²+(distance)²,where the speed costs are summed over all time progression points,speed′ denotes an acceleration value or a cost to change speed betweentwo adjacent points, speed″ denotes a jerk value, or a derivative of theacceleration value or a cost to change the acceleration between twoadjacent points, and distance denotes a distance from the ST point tothe destination location. Here, the speed costs module calculates astation-time graph by minimizing the speed cost using quadraticprogramming optimization, for example, by the QP module.

Aggregator 411 performs the function of aggregating the path and speedplanning results. For example, in one embodiment, aggregator 411 cancombine the two-dimensional ST graph and SL map into a three-dimensionalSLT graph. In another embodiment, aggregator 411 can interpolate (orfill in additional points) based on two consecutive points on an SLreference line or ST curve. In another embodiment, aggregator 411 cantranslate reference points from (S, L) coordinates to (x, y)coordinates. Trajectory generator 413 can calculate the final trajectoryto control ADV 510. For example, based on the SLT graph provided byaggregator 411, trajectory generator 413 calculates a list of (x, y, T)points indicating at what time should the ADC pass a particular (x, y)coordinate.

Thus, path decision module 403 and speed decision module 405 areconfigured to generate a rough path profile and a rough speed profiletaking into consideration obstacles and/or traffic conditions. Given allthe path and speed decisions regarding the obstacles, path planningmodule 407 and speed planning module 409 are to optimize the rough pathprofile and the rough speed profile in view of the obstacles using QPprogramming to generate an optimal trajectory with minimum path costand/or speed cost.

FIG. 5 is a block diagram illustrating a station-lateral map accordingto one embodiment. Referring to FIG. 5 , SL map 500 has an S horizontalaxis, or station, and an L vertical axis, or lateral. As describedabove, station-lateral coordinates are a relative geometric coordinatesystem that references a particular stationary point on a reference lineand follows the reference line. For example, a (S, L)=(1, 0) coordinatecan denote one meter ahead of a stationary point (i.e., a referencepoint) on the reference line with zero meter lateral offset. A (S,L)=(2, 1) reference point can denote two meters ahead of the stationaryreference point along the reference line and an one meter perpendicularlateral offset from the reference line, e.g., a left offset.

Referring to FIG. 5 , SL map 500 includes reference line 501 andobstacles 503-509 perceived by ADV 510. In one embodiment, obstacles503-509 may be perceived by a RADAR or LIDAR unit of ADV 510 in adifferent coordinate system and translated to the SL coordinate system.In another embodiment, obstacles 503-509 may be artificially formedbarriers as constraints so the decision and planning modules would notsearch in the constrained geometric spaces. In this example, a pathdecision module can generate decisions for each of obstacles 503-509such as decisions to avoid obstacles 503-508 and nudge (approach veryclosely) obstacle 509 (i.e., these obstacles may be other cars,buildings and/or structures). A path planning module can thenrecalculate or optimize reference line 501 based on a path cost in viewof obstacles 503-509 using QP programming to fine tune reference line501 with the minimum overall cost as described above. In this example,the ADV nudges, or approaches very close, for obstacle 509 from the leftof obstacle 509.

FIGS. 6A and 6B are block diagrams illustrating station-time mapsaccording to some embodiments. Referring to FIG. 6A, ST graph 600 has astation (or S) vertical axis and a time (or T) horizontal axis. ST graph600 includes curve 601 and obstacles 603-607. As described above, curve601 on station-time graph indicates, at what time and how far away isthe ADV from a station point. For example, a (T, S)=(10000, 150) candenote in 10000 milliseconds, an ADV would be 150 meters from thestationary point (i.e., a reference point). In this example, obstacle603 may be a building/structure to be avoided and obstacle 607 may be anartificial barrier corresponding to a decision to overtake a movingvehicle.

Referring to FIG. 6B, in this scenario, artificial barrier 605 is addedto the ST graph 610 as a constraint. The artificial barrier can beexamples of a red light or a pedestrian in the pathway that is at adistance approximately S2 from the station reference point, as perceivedby the ADV. Barrier 705 corresponds to a decision to “stop” the ADVuntil the artificial barrier is removed at a later time (i.e., thetraffic light changes from red to green, or a pedestrian is no longer inthe pathway).

FIGS. 7A-7B are block diagrams illustrating speed versus distance plotsfor a speed limit change according to some embodiments. Referring toFIG. 7A, plot 700 can represent an ADV 101 on an expressway with aposted speed limit 721. The ADV 101 may have a planned route to exit anoff-ramp having a posted speed limit 723. Here, the posted speed limit721 of 100 km/h is about to change to 40 km/h and ADV 101 may becruising at a speed (such as ˜90 km/h) just below the posted speed limit721 of 100 km/h.

In one embodiment, ADV 101 may retrieve the posted road speed limit 721for the current section of the road from map & route data 311 or speedlimit information 313 of FIG. 3A. based on a planned path, ADV 101 cangenerate one or more speed curve (or trajectory) candidates and selectsone of the candidates based on a speed planning cost function. The speedplanning cost function may be:speedcost=Σ_(points)(speed′)²+Σ_(points)(speed″)²+(distance)²+cost(speedlimit);If speed>road speed limit,cost(speed limit)=max value(e.g.,1.0e9),where speed is a current speed of ADV 101, road speed limit is a postedroad speed limit for a road at a current location of the ADV, and maxvalue is set to some large value (e.g., 1.0e9).

Note that a trajectory may be generated for each planning cycle (e.g.,100 ms) and the planning cycle generates the trajectory for a planningwindow 725. For example, window 725 may be 8 seconds and ADV 101 cangenerate a trajectory for any planning cycle for the upcoming 8 seconds.

At a planning cycle that is approximately 8 seconds from a start ofposted speed limit 723, ADV 101 plans a trajectory with a change inspeed limit. That is, ADV 101 has an 8 seconds window to reduce a speedof ADV 101, in most cases, causing ADV 101 to apply a brake abruptly soa planned speed of ADV 101 will be below the post speed limit 723 whenADV 101 reaches the posted speed limit sign for speed limit 723. Here,ADV 101 may follow route 701 with an abrupt speed change right beforethe posted speed limit 723.

Referring to FIG. 7B, plot 710 may represent plot 700 of FIG. 7A but ADV101 plans a trajectory according to the posted speed limits 721, 723,and tapered speed limit 727. In one embodiment, ADV 101 may retrieve theposted road speed limit 721 and tapered speed limit 727 from map & routedata 311 or speed limit information 313 of FIG. 3A. The tapered speedlimit 727 may be over a road section of 500 meters with suggested speedlimits of 90 km/h (at 500 m), 80 km/h (at 400 m), 70 km/h (at 300 m), 60km/h (at 200 m), 50 km/h (at 100 m), and 40 km/h (at Om from theboundary of the speed limit change). ADV 101 then plans a trajectorybased on a modified speed planning cost function having a costcorresponding to both the road speed limit 721, 723, and/or taperedspeed limit 727 for a planning window 725. The modified speed planningcost function may be:speedcost=Σ_(points)(speed′)²+Σ_(points)(speed″)²+(distance)²+cost(speedlimit);If speed>road speed limit,cost(speed limit)=max value(e.g.,1.0e9);If speed<tapered speed limit,cost(speed limit)=0; andIf road speed limit>speed>tapered speed limit,cost(speedlimit)=α(speed−tapered speed limit),where speed is a current speed of ADV 101, road speed limit is a postedroad speed limit for a road at a current location of the ADV, taperedspeed limit is the tapered speed limit, max value is set to some largevalue (e.g., 1.0e9), and a is a scaling factor.

In one embodiment, based on a path route, ADV 101 generates one or morespeed curves and selects one speed curve based on the modified speedplanning cost function. In one embodiment, if ADV 101 is planned toovertake a vehicle, the scaling factor α may be adjusted such that acost associated with having a tapered speed limit is nullified and ADV101 can speed up to the posted road speed limit to overtake a vehicle.Note, the path route and one of the speed curve candidates can becombined to generate a trajectory candidate. ADV 101 then selects aspeed curve (or trajectory candidate) having the lowest cost based onthe modified speed planning cost function. The trajectory candidate isthen used to control ADV 101. Note that because ADV 101 can plan atrajectory based on a tapered speed limit, the planned trajectory cangradually reduce a speed of ADV 101 without apply a brake control (e.g.,tapered speed limit is generated with such a characteristic), and thus,ADV 101 speed planning can reduce a speed for ADV 101 without applying abrake control. That is, ADV 101 is not limited to the predeterminedspeed planning sliding window 725 of 8 seconds and a planned trajectorycan avoid an abrupt brake control.

FIGS. 8A-8B are block diagrams illustrating station-time maps accordingto some embodiments. FIG. 8A can correspond to FIG. 7A and FIG. 8B cancorrespond to FIG. 7B. Referring to FIG. 8A, ST graph 800 has a station(or S) vertical axis and a time (or T) horizontal axis. ST graph 800includes speed curve 801 and obstacles 821, 823. Obstacles 821, 823 mayrepresent artificial barriers corresponding to road speed limits 721(100 km/h) and 723 (40 km/h) of FIG. 7A, respectively. Here, slope 721for obstacle 821 is 100 km/h and slope 723 for obstacle 823 is 40 km/h.In one embodiment, ADV 101 generates one or more speed curves andselects curve 801 based on optimization of a speed planning costfunction. E.g., a hard constraint is applied such that slope of curve801 at points A, B should be less than slope 721; and the slope of curve801 at points C, D, E should be less than slope 723.

Here, because the slope between slope 721 and slope 723 is abrupt (e.g.,speed limit 100 km/h changes to 40 km/h), curve 801 includes an abruptspeed change (e.g., a sharp brake control). Thus, ADV 101 plans a speedcurve with an abrupt speed change.

Referring to FIG. 8B, in one embodiment, ST graph 810 may be similar toST graph 800 except ADV 101 takes into consideration a taper speedlimit. ST graph 810 includes speed curve 803 and obstacles 821, 823, and827. Obstacles 821, 823, and 827 may represent artificial barrierscorresponding to the road speed limits 721 (100 km/h), 723 (40 km/h);and tapered speed limit 727 of FIG. 7B, respectively.

In one embodiment, ADV 101 generates ST graph 810 for speed planning.Based on ST graph 810, one or more speed curve candidates (or trajectorycandidates) are generated at each planning cycle and one speed curve isselected as the optimal speed curve based on a modified speed planningcost function. For example, one or more speed curve candidates (notshown) can be generated at point A, and a curve from the candidates isselected as the optimal curve. Each curve may be selected along pointsA, B, C, D, and E for a speed curve 803. In one embodiment, a planningsystem of ADV 101 controls ADV 101 based on a selected speed curve (ortrajectory). Because the speed curve along points B and C is constrainedby tapered speed limit 827 (e.g., slope 727), curve along points B and Chas a gradual change in speed (e.g., a gradual deceleration). In oneembodiment, the gradual deceleration for the ADV 101 corresponds to adeceleration from a first speed limit of 100 km/h to a second speedlimit of 40 km/h without applying a brake while maintaining a samesteering for ADV 101.

FIG. 9 is a block diagram illustrating a speed limit module according toone embodiment. Speed limit module 308 can generate a number oftrajectory candidates based on a speed cost function, where a trajectorycandidate with the lower cost is selected to control an ADV. Referringto FIG. 9 , speed limit module 308 can include submodules such as speedlimits receiver 901, cost function determiner 902, costs determiner 903,speed curve/trajectory generator 904, and trajectory selector 905. Speedlimits receiver 901 can receive one or more speed limits from map data.The map data may be data streamed from a server (such as server 103 ofFIG. 1 ), or data local to ADV 101, such as map and route data 311 ofFIG. 3A. The speed limits may be posted road legal (maximum or minimum)speed limits or tapered (gradual slow down) speed limits associated witha steep drop in speed limits for sections of a road.

Cost function determiner 902 can determine a speed cost function foroptimization to calculate one or more trajectory (or speed curve)candidates. Costs determiner 903 can determine a cost associated witheach trajectory candidate. Speed curve/trajectory candidate generator904 can generate one or more trajectory candidates. trajectory selector905 can select one of the trajectory candidates as the trajectory tocontrol the ADV 101. Here, trajectories are path routes having speedinformation along the path routes (or a path route combined with a speedcurve) such that the planning system of an ADV can control the ADVautonomously.

FIG. 10 is a flow diagram illustrating a speed planning with gradualspeed limits method according to one embodiment. Processing 1000 may beperformed by processing logic which may include software, hardware, or acombination thereof. For example, process 1000 may be performed by speedlimit module 308 of FIG. 9 . Referring to FIG. 10 , at block 1001,processing logic receives speed limit information for an autonomousdriving vehicle (ADV), where the speed limit information includes achanging road speed limit for a current road of the ADV. At block 1002,processing logic determines a tapered speed limit corresponding to thecurrent road based on the speed limit information, where the taperedspeed limit correspond to a gradual speed reduction from a first roadspeed limit to a second road speed limit. At block 1003, processinglogic determines a cost function based on the tapered speed limit andthe first and second road speed limits. At block 1004, processing logicgenerates a number of trajectory candidates based on the cost function.at block 1005, processing logic selects a trajectory based on thetrajectory candidates to control the ADV using the selected trajectory.

In one embodiment, the tapered speed limit is generated in response todetermining that the current road of the ADV has an impending reductionin road speed limits. In one embodiment, a speed planning system of theADV has a planning time window smaller than a time window required forthe ADV to slow down from the first road speed limit to the second roadspeed limit without applying a brake control.

In one embodiment, a cost of the cost function is set to a maximum costfor a trajectory candidate having a planned speed greater than a roadspeed limit for a corresponding section of the road. In one embodiment,a cost of the cost function is set to a zero cost for a trajectorycandidate having a planned speed less than the tapered speed limit.

In one embodiment, a cost of the cost function is set to a valueproportional to a difference of the planned speed and the tapered speedlimit for a trajectory candidate having a planned speed between thetapered speed limit and the road speed limit for the correspondingsection of the road. In one embodiment, the cost function includes jerk,acceleration, speed, and/or distance costs.

FIG. 11 is a block diagram illustrating a tapered speed limits generatoraccording to one embodiment. Tapered speed limits generator 125 cangenerate one or more tapered speed limits (offline) to supplement postedspeed limits of a roadway where there is a change in the posted speedlimit. The change in the posted speed limits can be a change from ahigher to a lower speed limit. Referring to FIG. 11 , tapered speedlimits generator 125 can include submodules such as reference speedcurve determiner 1101, road speed limit determiner 1102, speed curvegenerator 1103, and tapered speed limits generator 1104. Reference speedcurve determiner 1101 can determine a reference speed curve for an ADV.The reference speed curve is a speed curve collected by an operatorwhile operating a vehicle from a higher speed (e.g., 120 km/h) to alower speed (10 km/h). In on embodiment, the curve data can be collectedfrom a physics simulation for a vehicle operating from a higher speed(e.g., 120 km/h) to a lower speed (10 km/h). The data collected reflectsa vehicle having the throttle and brake control released whilemaintaining a steering to slow down the vehicle from the high speed tothe lower speed. A reference speed curve may be collected based on amodel, make, or type of vehicles, etc. For example, a first referencespeed curve may be used for sedans, while a second reference speed curveis used for trucks, etc.

Road speed limit determiner 1102 can determine (retrieve) the road speedlimits for a current road of the ADV. Road speed limit determiner 1102can also determine an impending change in the speed limit (e.g., from afirst road speed limit to a second road speed limit) based on theretrieved road speed limits. Based on the impending change, speed curvegenerator 1103 can generate a speed curve by truncating/snipping thereference speed curve at a first point corresponding to the first speedlimit, and at a second point corresponding to the second speed limit.

Tapered speed limits generator 1104 can map the generated speed curve toa road segment before the point of change in speed limit, e.g., to theroad segment corresponding to the higher speed limit, such that thespeed curve corresponds to a vehicle gradually slowing down from thefirst speed limit to the second speed limit. Tapered speed limitsgenerator 1104 can generate a number of speed limits (e.g., taperedspeed limits) based on the speed curve and store it as part of speedlimit information so an ADV using the speed limit information has accessto both the tapered speed limit and the posted road speed limit.

FIG. 12 is a flow diagram illustrating a method to generate gradualspeed limits according to one embodiment. Processing 1200 may beperformed by processing logic which may include software, hardware, or acombination thereof. For example, process 1200 may be performed bytapered speed limits generator 125 of FIG. 11 . Referring to FIG. 12 ,at block 1201, processing logic determines a reference speed curve togradually slow down an autonomous driving vehicle (ADV). At block 1202,for each section of a plurality of road sections in speed limitinformation for an ADV, processing logic determines a reduction in speedlimit for the road section from a first speed limit to a second speedlimit. At block 1203, processing logic generates a tapered speed limitfor the road section from the first speed limit to the second speedlimit based on the reference speed curve. At block 1204, processinglogic stores the tapered speed limit for the section of road in thespeed limit information, where the tapered speed limit is used by theADV to generate driving trajectory candidates.

In one embodiment, the reference speed curve to gradually slow down anADV corresponds to a speed curve to slow down an ADV with a throttle anda brake control of the ADV released while maintaining a same steeringfor the ADV. In one embodiment, the tapered speed limit is generated bytruncating the reference speed curve starting at a speed correspondingto the first road speed limit and ending at a speed corresponding to thesecond road speed limit.

In one embodiment, the tapered speed limit includes a number of speedlimits at a number of points along the road section. In one embodiment,the tapered speed limit is used to generate a number of trajectorycandidates based on a cost function.

In one embodiment, one of the trajectory candidates is selected as atrajectory having a lowest cost to control the ADV based on the selectedtrajectory. In one embodiment, a cost of the cost function is set to amaximum cost if a trajectory candidate has a planning speed greater thana road speed limit for a corresponding section of the road.

Note that some or all of the components as shown and described above maybe implemented in software, hardware, or a combination thereof. Forexample, such components can be implemented as software installed andstored in a persistent storage device, which can be loaded and executedin a memory by a processor (not shown) to carry out the processes oroperations described throughout this application. Alternatively, suchcomponents can be implemented as executable code programmed or embeddedinto dedicated hardware such as an integrated circuit (e.g., anapplication specific IC or ASIC), a digital signal processor (DSP), or afield programmable gate array (FPGA), which can be accessed via acorresponding driver and/or operating system from an application.Furthermore, such components can be implemented as specific hardwarelogic in a processor or processor core as part of an instruction setaccessible by a software component via one or more specificinstructions.

Some portions of the preceding detailed descriptions have been presentedin terms of algorithms and symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptions andrepresentations are the ways used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of operations leading to adesired result. The operations are those requiring physicalmanipulations of physical quantities.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as those set forth in the claims below, refer to the actionand processes of a computer system, or similar electronic computingdevice, that manipulates and transforms data represented as physical(electronic) quantities within the computer system's registers andmemories into other data similarly represented as physical quantitieswithin the computer system memories or registers or other suchinformation storage, transmission or display devices.

Embodiments of the disclosure also relate to an apparatus for performingthe operations herein. Such a computer program is stored in anon-transitory computer readable medium. A machine-readable mediumincludes any mechanism for storing information in a form readable by amachine (e.g., a computer). For example, a machine-readable (e.g.,computer-readable) medium includes a machine (e.g., a computer) readablestorage medium (e.g., read only memory (“ROM”), random access memory(“RAM”), magnetic disk storage media, optical storage media, flashmemory devices).

The processes or methods depicted in the preceding figures may beperformed by processing logic that comprises hardware (e.g. circuitry,dedicated logic, etc.), software (e.g., embodied on a non-transitorycomputer readable medium), or a combination of both. Although theprocesses or methods are described above in terms of some sequentialoperations, it should be appreciated that some of the operationsdescribed may be performed in a different order. Moreover, someoperations may be performed in parallel rather than sequentially.

Embodiments of the present disclosure are not described with referenceto any particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof embodiments of the disclosure as described herein.

In the foregoing specification, embodiments of the disclosure have beendescribed with reference to specific exemplary embodiments thereof. Itwill be evident that various modifications may be made thereto withoutdeparting from the broader spirit and scope of the disclosure as setforth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

What is claimed is:
 1. A computer-implemented method to operate anautonomous driving vehicle (ADV), comprising: receiving speed limitinformation for an autonomous driving vehicle (ADV), wherein the speedlimit information includes a decrease in road speed limit for a currentroad of the ADV; determining a tapered speed limit corresponding to thecurrent road based on the speed limit information, wherein the taperedspeed limit indicates a gradual speed reduction starting at a first roadspeed limit and decreasing to a second road speed limit; determining acost function based on the tapered speed limit and the first and secondroad speed limits; generating a plurality of trajectory candidates basedon the cost function; and selecting a trajectory based on the trajectorycandidates to control the ADV using the selected trajectory, wherein theselected trajectory gradually reduces a speed of the ADV from the firstroad speed limit to the second road speed limit.
 2. The method of claim1, wherein the tapered speed limit is generated in response todetermining that the current road of the ADV has an impending reductionin road speed limits.
 3. The method of claim 1, wherein the ADV has aspeed planning time window smaller than a time window required for theADV to slow down from the first road speed limit to the second roadspeed limit without applying a brake control.
 4. The method of claim 1,wherein a cost of the cost function is set to a maximum cost for atrajectory candidate having a planned speed greater than a road speedlimit for a corresponding section of the current road.
 5. The method ofclaim 1, wherein a cost of the cost function is set to a zero cost for atrajectory candidate having a planned speed less than the tapered speedlimit.
 6. The method of claim 1, wherein a cost of the cost function isset to a value proportional to a difference of a planned speed and thetapered speed limit for a trajectory candidate having a planned speedbetween the tapered speed limit and the road speed limit for acorresponding section of the current road.
 7. The method of claim 1,wherein the cost function is selected from the group consisting of ajerk, an acceleration, a speed, a distance, and one or more speed limitcosts.
 8. A non-transitory machine-readable medium having instructionsstored therein, which when executed by a processor, cause the processorto perform operations, the operations comprising: receiving speed limitinformation for an autonomous driving vehicle (ADV), wherein the speedlimit information includes a decrease in road speed limit for a currentroad of the ADV; determining a tapered speed limit corresponding to thecurrent road based on the speed limit information, wherein the taperedspeed limit indicates a gradual speed reduction starting at a first roadspeed limit and decreasing to a second road speed limit; determining acost function based on the tapered speed limit and the first and secondroad speed limits; generating a plurality of trajectory candidates basedon the cost function; and selecting a trajectory based on the trajectorycandidates to control the ADV using the selected trajectory, wherein theselected trajectory gradually reduces a speed of the ADV from the firstroad speed limit to the second road speed limit.
 9. The non-transitorymachine-readable medium of claim 8, wherein the tapered speed limit isgenerated in response to determining that the current road of the ADVhas an impending reduction in road speed limits.
 10. The non-transitorymachine-readable medium of claim 8, wherein the ADV has a speed planningtime window smaller than a time window required for the ADV to slow downfrom the first road speed limit to the second road speed limit withoutapplying a brake control.
 11. The non-transitory machine-readable mediumof claim 8, wherein a cost of the cost function is set to a maximum costfor a trajectory candidate having a planned speed greater than a roadspeed limit for a corresponding section of the current road.
 12. Thenon-transitory machine-readable medium of claim 8, wherein a cost of thecost function is set to a zero cost for a trajectory candidate having aplanned speed less than the tapered speed limit.
 13. The non-transitorymachine-readable medium of claim 8, wherein a cost of the cost functionis set to a value proportional to a difference of the planned speed andthe tapered speed limit for a trajectory candidate having a plannedspeed between the tapered speed limit and the road speed limit for acorresponding section of the current road.
 14. The non-transitorymachine-readable medium of claim 8, wherein the cost function isselected from the group consisting of a jerk, an acceleration, a speed,a distance, and one or more speed limit costs.
 15. Acomputer-implemented method, comprising: determining a reference speedcurve to gradually slow down an autonomous driving vehicle (ADV); foreach section of a plurality of road sections in speed limit informationfor an ADV, determining a reduction in speed limit for the road sectionfrom a first road speed limit to a second road speed limit; generating atapered speed limit for the road section from the first road speed limitand gradually decreasing to the second road speed limit based on thereference speed curve; and storing the tapered speed limit for the roadsection in the speed limit information, wherein the tapered speed limitis used by the ADV to generate driving trajectory candidates.
 16. Thecomputer-implemented method of claim 15, wherein the reference speedcurve corresponds to a speed curve to slow down an ADV with a throttleand a brake control of the ADV released while maintaining a samesteering for the ADV.
 17. The computer-implemented method of claim 15,wherein the tapered speed limit is generated by truncating the referencespeed curve starting at a speed corresponding to the first road speedlimit and ending at a speed corresponding to the second road speedlimit.
 18. The computer-implemented method of claim 15, wherein thetapered speed limit indicates a plurality of speed limits at a pluralityof points along the road section.
 19. The computer-implemented method ofclaim 15, wherein the tapered speed limit is used to generate aplurality of trajectory candidates based on a cost function.
 20. Thecomputer-implemented method of claim 19, wherein one of the plurality oftrajectory candidates is selected as a trajectory having a lowest costto control the ADV based on the selected trajectory.